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Extended optimal preventive replacement policies with random working cycle

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  • Sheu, Shey-Huei
  • Liu, Tzu-Hsin
  • Zhang, Zhe-George

Abstract

This paper investigates the preventive replacement policies for an operating system that works for projects at random times. The system is subject to shocks which arrive according to a non-homogeneous Poisson process. When a shock takes place, the system is either replaced by a new one (type 2 failure) or minimally repaired (type 1 failure). The decision to repair or replace the system depends on the number of shocks that have occurred since the last replacement. In this paper, we propose the following two preventive replacement models: (1) the system is preventively replaced before a type 2 failure at age T or at the completion of the Nth working projects or at the kth type 1 failure, whichever occurs last; (2) the system is preventively replaced before a type 2 failure at age T or at the completion of the Nth working projects or at the kth type 1 failure, whichever occurs first. For each model, the optimum preventive replacement schedule that minimizes the long term expected cost per unit time is theoretically presented. Finally, we offer a computational algorithm for determining the optimum replacement policies, and we give a numerical example to illustrate our proposed models. This study provides a general framework such that many existing models are the special cases of the proposed models.

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  • Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George, 2019. "Extended optimal preventive replacement policies with random working cycle," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 398-415.
    • Handle: RePEc:eee:reensy:v:188:y:2019:i:c:p:398-415
    DOI: 10.1016/j.ress.2019.03.036
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    9. Lijun Shang & Xiguang Yu & Liying Wang & Yongjun Du, 2022. "Design of Random Warranty and Maintenance Policy: From a Perspective of the Life Cycle," Mathematics, MDPI, vol. 10(20), pages 1-22, October.
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    11. Xufeng Zhao & Mingchih Chen & Toshio Nakagawa, 2022. "Periodic replacement policies with shortage and excess costs," Annals of Operations Research, Springer, vol. 311(1), pages 469-487, April.
    12. Lijun Shang & Yongjun Du & Cang Wu & Chengye Ma, 2022. "A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    13. Lijun Shang & Xiguang Yu & Yongjun Du & Anquan Zou & Qingan Qiu, 2022. "An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge," Mathematics, MDPI, vol. 10(18), pages 1-19, September.
    14. Lijun Shang & Guojun Shang & Yongjun Du & Qingan Qiu & Li Yang & Qinglai Dong, 2022. "Post-Warranty Replacement Models for the Product under a Hybrid Warranty," Mathematics, MDPI, vol. 10(10), pages 1-18, May.
    15. Yongjun Du & Lijun Shang & Qingan Qiu & Li Yang, 2022. "Optimum Post-Warranty Maintenance Policies for Products with Random Working Cycles," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    16. Levitin, Gregory & Xing, Liudong & Xiang, Yanping, 2021. "Optimal multiple replacement and maintenance scheduling in two-unit systems," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    17. Chengye Ma & Yongjun Du & Lijun Shang & Li Yang & Kaiye Gao, 2023. "Random Maintenance Strategy Modeling of Warranted Products with Reliability Heterogeneity," Sustainability, MDPI, vol. 15(18), pages 1-19, September.
    18. Zhang, Qin & Fang, Zhigeng & Cai, Jiajia, 2021. "Preventive replacement policies with multiple missions and maintenance triggering approaches," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    19. Sheu, Shey-Huei & Liu, Tzu-Hsin & Sheu, Wei-Teng & Zhang, Zhe-George & Ke, Jau-Chuan, 2021. "Optimal replacement policy with replacement last under cumulative damage models," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    20. Shen, Jingyuan & Hu, Jiawen & Ma, Yizhong, 2020. "Two preventive replacement strategies for systems with protective auxiliary parts subject to degradation and economic dependence," Reliability Engineering and System Safety, Elsevier, vol. 204(C).

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